Essential Extensions and Injective Hulls of Fuzzy Modules

Margaret I. Doig and D. S. Malik ()
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Margaret I. Doig: Department of Mathematics, Creighton University, Omaha NE-68178, USA
D. S. Malik: Department of Mathematics, Creighton University, Omaha NE-68178, USA

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 527-539

Abstract: In this paper, we introduce the notion of essential extensions of fuzzy modules. We use these concepts to introduce the notion of injective hulls of fuzzy modules. It is known that every R-module has an injective hull, where R is a ring. We show that these corresponding results do not hold for fuzzy R-modules, i.e. there exists a fuzzy R-module that does not have an injective hull. Sufficient conditions are given for a fuzzy R-module to have an injective hull.

Keywords: Algebra; fuzzy module; fuzzy homomorphism; essential extension; injective hull (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500231

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